What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Can you fit the tangram pieces into the outline of Mai Ling?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

What is the greatest number of squares you can make by overlapping three squares?

Can you fit the tangram pieces into the outlines of the chairs?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Can you fit the tangram pieces into the outline of this junk?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you fit the tangram pieces into the outline of the rocket?

Can you fit the tangram pieces into the outline of this plaque design?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of Little Ming?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you fit the tangram pieces into the outline of this telephone?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Exchange the positions of the two sets of counters in the least possible number of moves

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you cut up a square in the way shown and make the pieces into a triangle?

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of these clocks?

Which of these dice are right-handed and which are left-handed?

Can you fit the tangram pieces into the outlines of these people?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

Can you fit the tangram pieces into the outline of these convex shapes?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.